Chances of lung damage from breast cancer radiation?

Low, but depends. The overall risk of lung damage resulting in breathing problems is less than 1-2%, but depends on the size of the radiation field, whether nodes are being treated, the technique (2d, 3d, or imrt), use of chemo during radiation (unusual), and issues with the patient (history of interstitial lung disease , etc). Ask your doctor what techniques they will use to reduce the amount of lung treated.
Slight. With modern techniques relatively uncommon, although x ray changes may occur more often than symptoms. Like anything else in the chest, side effects are greater in smokers.